This invention relates to an apparatus for performing two and/or three-dimensional nuclear magnetic resonance (NMR) imaging, which imaging is based upon a function of the spin density distribution, the spin-lattice relaxation time (T.sub.1) and the spin-spin relaxation time (T.sub.2) of particular protons within a target. More specifically, the invention relates to a NMR imaging method and apparatus which eliminates an additional unknown phase factor which originates from basic field inhomogeneities and field drifts and from non-perfect adjustment of electronic equipment.
Atomic nuclei have net magnetic moments when placed in a static magnetic field, B.sub.O, at an NMR (Larmor) frequency .omega. given by the equation EQU .omega.=.gamma.B.sub.O
in which .gamma. is the gyro-magnetic ratio, constant for each NMR isotope. The frequency at which the nuclei precess is primarily dependent on the strength of the magnetic field B.sub.O, and increases with increasing field strength.
Many different techniques are currently being investigated by which a characteristic image of a target, which might be part of a patient, can be effectively and efficiently obtained by nuclear magnetic resonance (NMR) imaging. Typically, the characteristic sought to be obtained is some function of the spin density distribution, the spin-lattice relaxation time (T.sub.1) and the spin-spin relaxation time (T.sub.2) of particular protons within the target. These protons are first excited by application of a magnetic field and a radio frequency (RF) pulse. Protons thus excited tend subsequently to relax, and during the process of relaxing generate a free induction decay (FID) signal. The above characteristic function of the relaxing protons within the target may be obtained by a Fourier transformation of this FID signal. By using the RF pulse chosen to have a selected frequency spectrum corresponding to the Larmor frequency of the protons given by the formula .omega.=.gamma.B.sub.O, it is possible to excite protons in a single plane which may be a slice of the patient target.
Imaging techniques utilizing NMR may typically be classified as imaging from projections, and direct mapping.
The technique of imaging from projections (i.e., projection reconstructions) entails producing a multiplicity of projections from many different orientations by, for example, generating a linear field gradient within the object and recording a one dimensional projection of nuclear density in the direction defined by the gradient. An image is then reconstructed from the projections by mathematical techniques similar to those used X-ray tomography. Such a method is described, for example, by Lauterbur, Nature, 249-190, March 1973.
Direct mapping or Fourier imaging techniques generally employ an initial RF pulse to reorient the spins of the protons in the object by 90.degree.. During the resultant FID signal, the object is subject to gradients applied consecutively in quick succession along the three principal Cartesian axes of the system. The FID and/or spin-echo signals are sampled, and a three dimensional Fourier transform is performed to develop a three dimensional image. Two dimensional Fourier transform methods are also known. In U.S. Pat. No. 4,070,611, incorporated herein by reference, there is described a method of producing images by the Fourier NMR technique. A general discussion of various projection and direct mapping techniques may be found in Chapter 35 of Nuclear Magnetic Resonance NMR Imaging, Partain et al, W. B. Saunders Company 1983, incorporated herein by reference.
The present invention is directed to a technique utilizing Fourier transformations with the production of images of samples. The spatial density distribution of these samples may be determined from the observed free induction decays (FID's) and/or spin echoes of the sample in the presence of static magnetic fields and switched magnetic field gradients.
The pulse sequence used to form an image by a Fourier-based NMR imaging method is shown in FIG. 1.
A single plane is first selected by application of a narrow band 90.degree. RF pulse and field gradient G.sub.z. Two-dimensional FID sets are then obtained by varying t.sub.x or the pulse length of G.sub.x. The function of the gradient is to provide discrimination in the Y direction. It is introduced to give a known amount of twist or warp to each vertical column of spins (Y axis being vertical), and thus it phase encodes the signal prior to projection onto the X axis. Spin echoes are produced by application of 180.degree. RF pulse. The G.sub.z pulse following application of the 180.degree. pulse serves to refocus the spins oriented in the x,y plane. The entire set of steps described above is successively repeated a number of times, N, and in each repetition, a different amplitude of gradient G.sub.y is utilized to cover a range of vertical spatial frequencies from zero up to a maximum. The projected spin density values for any one column to be obtained from the Fourier transforms of the spin-echo signals are arranged in order of increasing G.sub.y pulse size, and subjected to another Fourier transform for representing the distribution of spin density up the column. When this is done for each column a complete two-dimensional image of the selected slice is obtained. The phase-encoding gradient G.sub.y causes N different projections to be collected onto the X axis, because spins at different heights are given varying amounts of phase twist by the presence of different values of G.sub.y.
The phase information in an NMR signal is preserved by employing two phase-sensitive detectors in quadrature to produce two signals which are complex conjugate pairs.
The two signals obtained after quadrature-detection are written as follows after the Fourier transformation: EQU E(k.sub.x,k.sub.y)=.intg..intg.f(x,y) exp [i(k.sub.x x+k.sub.y y)]dxdy (1)
in which EQU k.sub.x =.gamma.G.sub.x .multidot.t
and EQU k.sub.y =.gamma..multidot.n.multidot.(G.sub.y /N).multidot.t
The function f(x,y) gives the spatial distributions. The spatial frequencies k.sub.x and k.sub.y describe the wave numbers of the respective direction, x,y, and n an integral sampling index within the range -NL or LN, N being an integer.
However, in practice, there is added to the above ideal signal an additional unknown phase factor which originates from basic field inhomogeneities and field drifts and from non-perfect electronics adjustment.
Therefore, Eq. (1) can be rewritten as EQU E'(k.sub.x, k.sub.y)=.intg..intg.f(x,y) exp [i(k.sub.x x+k.sub.y +.theta.)]dxdy (2)
The distribution of a nuclear resonance parameter as a function of the location (x,y) is given by EQU f'(x,y)=f(x,y) exp [i.theta.] (3)
Because one would have to take the real part of a complex two-dimensional Fourier-transformed signal, the "absorption", as an image value, and one would have to reject the imaginary component, the "dispersion", since the latter, on account of its broad wings, is not suitable for imaging, it is proposed that the distribution can be calculated by obtaining an absolute value of Eq. (3) as follows: EQU f(x,y)=.vertline.f'(x,y).vertline.=.vertline.f'(x,y)e.sup.i.theta. .vertline. (4)
For these calculation steps, much time is consumed. Further the negative wings of the imaginary component are not useful for image information.
It is also noted in the case of use of the spin echo technique, there exist a point symmetry with respect to the point k.sub.x =k.sub.y =0 of the (k.sub.x,k.sub.y) space formed by the spatial frequencies as illustrated in FIG. 2. Thus, actually sampling operations are required, for example, either for all k.sub.x, where k.sub.y .gtoreq.0, or for all k.sub.y, where k.sub.x .gtoreq..theta.. Such symmetry reduces the sampling period up to one half. Thus EQU E(-k.sub.x,-k.sub.y)=[E(k.sub.x,k.sub.y)]* (5)
where "*" means a complex conjugate pair.
If the phase factor is considered in this method, Eq. (2) is defined as follows: EQU E(-k.sub.x,-k.sub.y)=exp (-i.theta.)[E(k.sub.x,k.sub.y)]*.noteq.[E(k.sub.x,k.sub.y)]* (6)
As understood from the above expression, it is not expected that one may shorten the sampling period for all desired sampling data by utilization of the point symmetry in the (k.sub.x,k.sub.y) space where the phase factor is taken into consideration.